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A349506
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a(n) is the numerator of n!^(2*n)/(n^n^2).
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7
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1, 1, 64, 6561, 63403380965376, 1000000000000, 10061319724179153710638694400000000000000, 9396559338406702410023114843902587890625, 528450425551613768181656289451784661530463698944000000000000000000, 13597557929083423616920569866317288159544321459878738801559053666747416576
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OFFSET
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1,3
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COMMENTS
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a(n) is the numerator of a lower bound of the number of the vertices of the polytope of stochastic semi-magic n X n X n cubes, or equivalently, of the number of Latin squares of order n, or equivalently, of the number of n X n X n line-stochastic (0,1)-tensors (see Ahmed et al. and Zhang et al.).
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LINKS
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FORMULA
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a(n)/A349507(n) ~ n^(-n^2)*(exp(-n)*n^(n-1/2)*(1+12*n))^(2*n)*(Pi/72)^n.
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MATHEMATICA
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Table[Numerator[n!^(2n)/(n^n^2)], {n, 10}]
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PROG
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(PARI) a(n) = numerator(n!^(2*n)/n^n^2); \\ Michel Marcus, Nov 22 2021
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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